Methods and apparatus are known by which images are produced representing the spin density distribution of selected nuclei in an object. For this purpose the free induction signals which are generated after nuclear magnetic resonance are detected in the presence of a magnetic field gradient. The detected signal is subjected to a Fourier transform operation to convert the signal from the time domain to the frequency domain and this gives a distribution of the spin density along the direction of the gradient. Various techniques are known by which a two dimensional image can be obtained. Thus, in one proposal a series of one dimensional projections of an object in different directions are obtained and an image is built up by projection reconstruction. In another technique, a slice in the object is preselected by selective irradiation as described in British Pat. No. 1525564, (corresponding to U.S. Pat. No. 4,021,726) also as described in examples in that patent an image of the slice can be built up line-by-line, or else for example an echo planar technique can be used as described in British Pat. No. 1596160 (corresponding U.S. Pat. No. 4,165,479) to obtain image information relating to an entire preselected slice. However, in all cases a Fourier transformation of the detected free induction signal must be carried out. While this can be readily achieved by the use of a digital computer, it requires a relatively expensive computer and takes a noticeable amount of time. This transformation step constitutes the most exacting technical requirement for the computer facilities in an imaging system.